Statistical properties of the quantile normalization method for density curve alignment
ABSTRACT: The article investigates the large sample properties of the quantile normalization method by Bolstad et al. (2003) [4] which has become one of the most popular methods to align density curves in microarray data analysis. We prove consistency of this method which is viewed as a particular c...
- Autores:
-
Gallón Gómez, Santiago Alejandro
Loubes, Jean Michel
Maza, Elie
- Tipo de recurso:
- Article of investigation
- Fecha de publicación:
- 2013
- Institución:
- Universidad de Antioquia
- Repositorio:
- Repositorio UdeA
- Idioma:
- eng
- OAI Identifier:
- oai:bibliotecadigital.udea.edu.co:10495/7347
- Acceso en línea:
- http://hdl.handle.net/10495/7347
- Palabra clave:
- Wasserstein distance
Curve registration
Manifold registration
Microarray data analysis
Normalization
Order statistics
Structural expectation
- Rights
- openAccess
- License
- Atribución 2.5
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| dc.title.spa.fl_str_mv |
Statistical properties of the quantile normalization method for density curve alignment |
| title |
Statistical properties of the quantile normalization method for density curve alignment |
| spellingShingle |
Statistical properties of the quantile normalization method for density curve alignment Wasserstein distance Curve registration Manifold registration Microarray data analysis Normalization Order statistics Structural expectation |
| title_short |
Statistical properties of the quantile normalization method for density curve alignment |
| title_full |
Statistical properties of the quantile normalization method for density curve alignment |
| title_fullStr |
Statistical properties of the quantile normalization method for density curve alignment |
| title_full_unstemmed |
Statistical properties of the quantile normalization method for density curve alignment |
| title_sort |
Statistical properties of the quantile normalization method for density curve alignment |
| dc.creator.fl_str_mv |
Gallón Gómez, Santiago Alejandro Loubes, Jean Michel Maza, Elie |
| dc.contributor.author.none.fl_str_mv |
Gallón Gómez, Santiago Alejandro Loubes, Jean Michel Maza, Elie |
| dc.subject.none.fl_str_mv |
Wasserstein distance Curve registration Manifold registration Microarray data analysis Normalization Order statistics Structural expectation |
| topic |
Wasserstein distance Curve registration Manifold registration Microarray data analysis Normalization Order statistics Structural expectation |
| description |
ABSTRACT: The article investigates the large sample properties of the quantile normalization method by Bolstad et al. (2003) [4] which has become one of the most popular methods to align density curves in microarray data analysis. We prove consistency of this method which is viewed as a particular case of the structural expectation procedure for curve alignment, which corresponds to a notion of barycenter of measures in the Wasserstein space. Moreover, we show that, this method fails in some case of mixtures, and we propose a new methodology to cope with this issue. |
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2013 |
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2013 |
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2017-05-24T21:59:16Z |
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2017-05-24T21:59:16Z |
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Gallón Gómez, S. A., Loubes, J. M. & Maza, E. (2013). Statistical properties of the quantile normalization method for density curve alignment. Mathematical Biosciences, 242(2), 129-142. |
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0025-5564 |
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http://hdl.handle.net/10495/7347 |
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Gallón Gómez, S. A., Loubes, J. M. & Maza, E. (2013). Statistical properties of the quantile normalization method for density curve alignment. Mathematical Biosciences, 242(2), 129-142. 0025-5564 |
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http://hdl.handle.net/10495/7347 |
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eng |
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eng |
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Atribución 2.5 |
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info:eu-repo/semantics/openAccess |
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Elsevier |
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Estados Unidos |
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Universidad de Antioquia |
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Gallón Gómez, Santiago AlejandroLoubes, Jean MichelMaza, Elie2017-05-24T21:59:16Z2017-05-24T21:59:16Z2013Gallón Gómez, S. A., Loubes, J. M. & Maza, E. (2013). Statistical properties of the quantile normalization method for density curve alignment. Mathematical Biosciences, 242(2), 129-142.0025-5564http://hdl.handle.net/10495/7347ABSTRACT: The article investigates the large sample properties of the quantile normalization method by Bolstad et al. (2003) [4] which has become one of the most popular methods to align density curves in microarray data analysis. We prove consistency of this method which is viewed as a particular case of the structural expectation procedure for curve alignment, which corresponds to a notion of barycenter of measures in the Wasserstein space. Moreover, we show that, this method fails in some case of mixtures, and we propose a new methodology to cope with this issue.13application/pdfengElsevierEstados Unidosinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://purl.org/coar/resource_type/c_2df8fbb1https://purl.org/redcol/resource_type/ARTArtículo de investigaciónhttp://purl.org/coar/version/c_970fb48d4fbd8a85Atribución 2.5info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/2.5/co/http://purl.org/coar/access_right/c_abf2https://creativecommons.org/licenses/by-nc-nd/4.0/Wasserstein distanceCurve registrationManifold registrationMicroarray data analysisNormalizationOrder statisticsStructural expectationStatistical properties of the quantile normalization method for density curve alignmentMathematical Biosciences1291422422ORIGINALGallonSantiago_2013_StatisticalPropertiesQuantile.pdfGallonSantiago_2013_StatisticalPropertiesQuantile.pdfArtículo de investigaciónapplication/pdf7268447http://bibliotecadigital.udea.edu.co/bitstream/10495/7347/1/GallonSantiago_2013_StatisticalPropertiesQuantile.pdf32f30ede8187333f619b29e75f152b23MD51CC-LICENSElicense_urllicense_urltext/plain; charset=utf-849http://bibliotecadigital.udea.edu.co/bitstream/10495/7347/2/license_url4afdbb8c545fd630ea7db775da747b2fMD52license_textlicense_texttext/html; charset=utf-80http://bibliotecadigital.udea.edu.co/bitstream/10495/7347/3/license_textd41d8cd98f00b204e9800998ecf8427eMD53license_rdflicense_rdfapplication/rdf+xml; charset=utf-80http://bibliotecadigital.udea.edu.co/bitstream/10495/7347/4/license_rdfd41d8cd98f00b204e9800998ecf8427eMD54LICENSElicense.txtlicense.txttext/plain; charset=utf-81748http://bibliotecadigital.udea.edu.co/bitstream/10495/7347/5/license.txt8a4605be74aa9ea9d79846c1fba20a33MD5510495/7347oai:bibliotecadigital.udea.edu.co:10495/73472021-06-13 12:40:17.143Repositorio Institucional Universidad de Antioquiaandres.perez@udea.edu.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 |